How to render as only wireframe in Cycles?
Add the Wireframe modifier and adjust the Thickness value.



Now set up the World's color to black and make the wire look brighter (replace Diffuse with an Emission shader). You may also increase its Strenght value to 2.000 or 3.000 if it isn't bright enough.



To vary between the smooth wireframe object and the polygonal wireframe object place the Subdivision Surface modifier above the Wireframe modifier and set up the desired amount of subdivisions. Now changing the type from Catmull-Clark to Simple will result in making the wire look more polygonal.


Here's the rendered result.